Not really an expert on the 737, but have you considered the idea that the hydraulic reservoirs need to be pressurized?
On the 767, each pneumatic duct will pressurize its respective hyd reservor - maybe this applies for the 737 aswell? (2 ducts - 2 hyd systems)
Should a hyd reservoir not be pressurized for a longer time, cavitation may occur (especially at high altitudes) which may cause damage to the hyd pumps.
Just a theory...
Regards,
Mark